Matrices de rotaciones, simetr\'ıas y roto-simetr\'ıas

In this note we find the orthogonal matrices $R,S\in M_3(\mathbb{R})$ corresponding to the clockwise rotation $r$ in $\mathbb{R}^3$ around the axis generated by a unit vector $u=(a,b,c)^t$ through an angle $α\in [0,2π)$, and to the symmetry $s$ in $\mathbb{R}^3$ on the plane perpendicular to $u$. Matrix $S$ depends on $a,b,c$ and matrix $R$ depends on $a,b,c, \cos α$ and $\sin α$. We show $SR=RS$. The matrix $R$ is due to Alperin.

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